Object exported as Obj looses textures in Unity
I'm a newbie too.  Almost all tutorials I've seen using Blender and Unity together use fbx files.  I don't know why and I don't know the relative advantages or .obj and .fbx, but maybe try exporting as an fbx (on the save screen, enable mesh, armature and material only).  This should at least export the material with the mesh, making it more likely they will be compatible...maybe.

Unity Result